| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch single transformation from given curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring only direct application of standard rules: horizontal translation and reflection. Students need to apply f(x+3) shifts left 3 units and f(-x) reflects in y-axis, then transform the given coordinates accordingly. No problem-solving or conceptual insight required beyond recalling these basic transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Shape \(\bigcup\!\!\!\!\nearrow\) touching \(x\)-axis at its maximum | M1 | Generous even if curve appears as straight line segments, but must show discernible curve at max and min. |
| Through \((0,0)\) and \(-3\) marked on \(x\)-axis, or \((-3,0)\) seen. Allow \((0,-3)\) if marked on \(x\)-axis. | A1 | 1st A1: curve passing through \(-3\) and the origin, max at \((-3,0)\). Marked in correct place; \(3\) is A0. |
| Min at \((-1,-1)\) | A1 | Can simply be indicated on sketch. (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Correct shape \(\bigvee\!\!\!\!\searrow\) (top left to bottom right) | B1 | Negative cubic passing top-left to bottom-right; must show discernible curve at max and min. |
| Through \(-3\) and max at \((0,0)\) | B1 | Curve passing through \((-3,0)\) having max at \((0,0)\) and no other max. Marked in correct place; \(3\) is B0. |
| Min at \((-2,-1)\) | B1 | No other minimum. If in correct quadrant but labelled e.g. \((-2,1)\), this is B0. (3 marks, [6] total) |
## Question 5:
**(a)**
Shape $\bigcup\!\!\!\!\nearrow$ touching $x$-axis at its maximum | M1 | Generous even if curve appears as straight line segments, but must show discernible curve at max and min.
Through $(0,0)$ and $-3$ marked on $x$-axis, or $(-3,0)$ seen. Allow $(0,-3)$ if marked on $x$-axis. | A1 | 1st A1: curve passing through $-3$ and the origin, max at $(-3,0)$. Marked in correct place; $3$ is A0.
Min at $(-1,-1)$ | A1 | Can simply be indicated on sketch. (3 marks)
**(b)**
Correct shape $\bigvee\!\!\!\!\searrow$ (top left to bottom right) | B1 | Negative cubic passing top-left to bottom-right; must show discernible curve at max and min.
Through $-3$ and max at $(0,0)$ | B1 | Curve passing through $(-3,0)$ having max at $(0,0)$ and no other max. Marked in correct place; $3$ is B0.
Min at $(-2,-1)$ | B1 | No other minimum. If in correct quadrant but labelled e.g. $(-2,1)$, this is B0. (3 marks, **[6]** total)5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{871f5957-180d-4379-88ce-186432f57bad-06_988_1158_285_390}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve $C$ with equation $y = \mathrm { f } ( x )$. There is a maximum at $( 0,0 )$, a minimum at $( 2 , - 1 )$ and $C$ passes through $( 3,0 )$.
On separate diagrams sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x + 3 )$,
\item $y = \mathrm { f } ( - x )$.
On each diagram show clearly the coordinates of the maximum point, the minimum point and any points of intersection with the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2009 Q5 [6]}}